Solving the 3x3 Real Symmetric Eigenproblem
This work provides a practical, specialized solution for a common numerical bottleneck in applications like finite element analysis, particularly enabling efficient GPU implementation.
The paper presents a tailored algorithm for solving the 3x3 real symmetric eigenproblem, designed to be compact and easily coded, with compatibility for GPU-based parallel processing to handle large numbers of such problems efficiently.
We develop an algorithm solving the 3x3 real symmetric eigenproblem. This is a common problem and in certain applications it must be solved many thousands of times, see for example \cite{tripref} where each element in a finite element grid generates one. Because of this it is useful to have a tailored method that is easily coded and compact. Furthermore, the method described is fully compatible with development as a GPU based code that would allow the simultaneous solution of a large number of these small eigenproblems.